Mechanics knowledge catalogue

Engineering topics

Browse engineering mechanics and strength of materials topics with interactive practice problems for students and teachers.

• ▾Theoretical Mechanics
  • ▾Statics
    • ▾Fundamentals of Forces and Moments
      • Basic Concepts of Statics. Force and Force Systems
      • Force Projections
      • Moment of a Force About a Point and an Axis
      • Force Couples and Couple Moment
      • Addition of Forces. Resultant of a Force System
      • Reduction of a Force System to a Given Point
    • ▾Equilibrium of Coplanar Systems
      • Equilibrium Conditions for Coplanar Force Systems
      • Constraints and Constraint Reactions
      • Equilibrium of a Rigid Body in Two Dimensions
      • Equilibrium of Systems of Bodies. Method of Disassembly
      • Distributed Loads and Their Resultants
    • ▾Three-Dimensional Statics
      • Three-Dimensional Force Systems
      • Equilibrium Conditions for Three-Dimensional Force Systems
      • Center of Parallel Forces and Center of Gravity
    • ▾Friction
      • Sliding Friction. Coulomb's Laws
      • Equilibrium with Friction
      • Rolling Resistance
  • ▾Kinematics
    • ▾Particle Kinematics
      • Particle Kinematics. Methods of Describing Motion
      • Particle Velocity
      • Particle Acceleration
      • Special Cases of Particle Motion
    • ▾Basic Motions of a Rigid Body
      • Translation of a Rigid Body
      • Rotation of a Rigid Body About a Fixed Axis
      • Velocities and Accelerations of Points in Fixed-Axis Rotation
      • Transmission of Rotational Motion
    • ▾Plane Motion of a Rigid Body
      • Plane Motion of a Rigid Body
      • Velocities of Points in Plane Motion
      • Accelerations of Points in Plane Motion
    • ▾Relative Motion of a Particle
      • Relative Motion of a Particle
      • Acceleration Addition. Coriolis Acceleration
    • ▾Spatial Motion of a Rigid Body
      • Spherical Motion of a Rigid Body
      • General Motion of a Free Rigid Body
  • ▾Dynamics
    • ▾Particle Dynamics
      • Fundamental Laws of Dynamics. Newton's Laws
      • Differential Equations of Motion of a Particle
      • Two Fundamental Problems of Particle Dynamics
      • Particle Motion Under Typical Forces
    • ▾General Theorems of Particle Dynamics
      • Linear Momentum of a Particle. Impulse of a Force
      • Angular Momentum of a Particle
      • Work of a Force. Power
      • Kinetic Energy of a Particle. Work-Energy Theorem
      • Potential Force Field. Potential Energy
      • Conservation of Mechanical Energy
    • ▾Dynamics of Mechanical Systems
      • Dynamics of a Mechanical System. Center of Mass
      • Theorem on the Motion of the Center of Mass
      • Impulse-Momentum Theorem for a Mechanical System
      • Angular-Momentum Theorem for a Mechanical System
      • Kinetic Energy of a Mechanical System
      • Work-Energy Theorem for a Mechanical System
    • ▾Analytical Mechanics and Oscillations
      • D'Alembert's Principle for a Particle and a System
      • Virtual Displacements. Principle of Virtual Work
      • General Equation of Dynamics
      • Lagrange's Equations of the Second Kind
      • Small Oscillations of a One-Degree-of-Freedom System
• ▾Strength of Materials
  • ▾Basic Concepts and Types of Deformation
    • Scope and Objectives of Strength of Materials
    • Deformation and Displacement
    • Elastic and Plastic Deformation
    • Basic Modes of Deformation
    • Strength, Stiffness and Stability
    • Basic Material Properties and Models
    • Composite Materials
    • Assumptions and Idealizations in Strength of Materials
    • Loads and Supports
    • Structural Element Models
    • External and Internal Forces. Method of Sections
    • Stress and Strain at a Point
  • ▾Tension and Compression
    • Internal Forces and Stresses in Cross-Sections
    • ▾Mechanical Properties of Materials
      • Tensile Test Diagram and Characteristic Points
      • Elastic Properties of Materials
      • Ductility and Brittleness of Materials
      • Allowable Stresses and Factor of Safety
      • Strain Hardening and Reloading
      • External Factors Affecting Mechanical Properties
    • Thermal Deformations and Stresses
    • Statically Indeterminate Problems under Axial Loading
    • Deformation of Bars in Tension and Compression
    • Strength and Stiffness Design in Tension and Compression
  • ▾Shear and Torsion
    • Pure Shear and Design of Joints (Riveted and Welded)
    • Torsion of Solid and Hollow Circular Shafts
    • Design of Helical Springs
    • Power Transmission by Shafts
  • ▾Stress and Strain State
    • Stress Analysis at a Point (Principal Stresses)
    • Strength Theories (Failure Criteria)
    • Generalized Hooke's Law
  • ▾Geometric Properties of Plane Areas
    • Centroid and First Moments of Area
    • Second and Polar Moments of Area
    • Parallel-Axis Theorem and Composite Sections
    • Product of Inertia and Axis Rotation
    • Principal Axes, Principal Moments, and Section Moduli
  • ▾Bending
    • Internal Forces in Bending
    • Stresses in Bending
    • ▾Deflections in Bending
      • Differential Equation of the Elastic Curve
      • Initial Parameter Method (Macaulay's Method)
  • ▾Combined Loading
    • Unsymmetrical Bending
    • Eccentric Compression
    • Combined Bending and Torsion
  • ▾Energy Methods
    • Work of External Forces and Strain Energy
    • Castigliano's Theorem and Mohr's Integral
  • ▾Stability of Compressed Members
    • Euler's Formula for Critical Load
    • Limits of Applicability of Euler's Formula (Yasinsky Formula)
  • ▾Dynamic and Cyclic Loading
    • Inertia Forces
    • Impact Loading Calculations
    • Material Fatigue and Endurance Limit
  • ▾Shell Analysis
    • Membrane Theory
  • ▾Contact Stresses
    • Contact of Two Bodies: Types and Geometry
    • Hertz Theory: Main Assumptions and Formulas
    • Contact of Spheres and Spherical Surfaces
    • Contact of Cylinders and Rollers
    • Stress State Beneath the Contact Surface
    • Contact Strength of Machine Elements
• ▾Structural Mechanics
  • Trusses
  • Frames